Inventing Moons and their Eclilpses-help

[Super**Nova]

Inventing Moons and their Eclilpses--help!

I'm not mathmatically inclined, but I don't mind learning.

I used the model of the typical eclipse seasons for Earth, and it works for Earth, but what about inventing a totally different planet with two moons? I hate guessing. I'm calculating an effect in a science fictoin story I'm writing that rides heavily on the eclipse cycles. I won't settle for the typical writer writing about a fluffy full moon off the top of their head, just because they feel like writing about the moon. I want real data.

I want both moons to eclipse at different times each, but what I can't firgure out for the life of me are their eclipse cycles (length of eclipse season per moon, how many seasons per year) and where the nodes would land per moon, per year, for at least 8 years.

The planet's orbit takes 722 days to complete.

I've figured out their average synodic months; moon one's synodic month is 48 days, its sidereal month is 45.2 days. Moon two's is 80 days, and its sidereal month lasts 72.5 days.
Moon one's orbit to the ecliptic is 6.8 degrees. Moon two's is 40.3 degrees to the ecliptic.

I can't give you numbers as to how far each of the moons are from the planet. I don't yet know the speed they travel. All I know is moon one is smaller and closer, and moon two is farther and MUCH larger, about half the size of the home planet. (Tell me that works for the data given.)

Help me understand something, here. If Earth's moon orbit was tilted at 7 degrees instead of 5, how would that affect the times of eclipse? 8 degrees? Why doesn't its orbit ever stay fixed all throughout the year--why, even though it's tilted 5 degrees, why aren't the eclipse seasons perfectly 6 months apart instead of 173 days? I just don't understand how that works. Why the moon's orbit steadily reverses every 9 years and returns to the same every 18.

Anyway, regarding my invented moons, the answers I'm most concerned with are:
1). How many days, for each moon, will one eclipse season last?
2). How many eclipse seasons per year, per moon?
3). How many days to the next eclipse season per moon?
4). How many solar eclipses can either moon get per season? How many lunar eclipses per season?

Based on what I posted, please show me how you arrived to your conclusion. I hope that wasn't too much. I do need the answers to all of those in the 2nd to last paragraph, at least.

Thank you.

 

[Janus]

I'll try to answer at least some of your questions.

You can find the distance of your moons from their orbital periods and the mass of the Planet with the following:

[tex]P = 2 \pi \sqrt{\frac{r^3}{G(M+m)}}[/tex]

Where P is the orbital period
r is radius of the orbit
G is the gravitational constant
[tex] =\ 6.673 \times\ 10^{-11}\ m^{3} kg^{-1} s^{-2}[/tex]

M is the mass of the planet.
m is the mass of the moon.

Just plug in the known values and solve for r.

The eclipse seasons do not occur exactly 6 months apart due to the precession of the Lunar nodes. Just like the axis of the Earth "wobbles" over time, so does the Moon's orbital plane. As a result, the points where the Moon's orbit crosses the ecliptic slowly shift westward. This means that the Sun arrives at the nodes a little earlier then otherwise. It takes about 18 yrs for the nodes to make a complete cycle and to return to the same positions, during this time, the eclipse seasons slowly shift through the year. This 18 year cycle is called the saros.

Your larger outer moon will likely have a strong effect on the precession of the nodes for the inner moon.

The tilt of the orbit will effect the timing of eclipses in that the tilt is a factor in how fast the nodes precess.
It also will effect the length of the season because it effects how long the moon stays close enough to the ecliptic for an eclipse to occur. The greater the angle, the shorter the eclipse season.

Another factor that is important is the apparent size of your moons. The larger the moon, the greater the chance of at least a partial eclipse. The apparent size will depend on the distance, mass and density of the moon.

 

[Super**Nova]

Your larger outer moon will likely have a strong effect on the precession of the nodes for the inner moon.

Wow, that helps a lot! Thank you so much.

Now, I have another question based off of that particular idea. By "effect on the precession of the nodes," because it's a larger outer moon to a smaller moon, does that equal to an increase in precession? Would it make the smaller moon's precession more erratic? Could it be possible to have more than 2 eclipse seasons per year? It seems reasonable.

How do I figure out the number of days in the planet's year to predict eclipse seasons? What equation do I follow? That's most important.

And as an off the wall question, does a circular orbit of a satillite necessarily have to remain the same distance from the planet as it makes a full orbit around the planet, an off-centered circular orbit, so that even with a circular orbit, it could hava an anomalistic month? Or, would that qualify it as an elliptical orbit? Does the angle to the ecliptic greater than 0° automatically give it an elliptical orbit, or can an angled orbit be independent of an elliptical path?

Thanks, again.